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Given that the 10th term of an AP is 45 and that the sum
of the first 10 terms is 270 find
a) The first term
b) The common difference
c) The sum of the first 15 terms

Respuesta :

A) The first term of the AP is; 9

B) The common difference of the AP is; 4

C) The sum of the first 15 terms of the AP is; 555

Formula for nth term of an AP is;

a_n = a + (n - 1)d

Where;

a is first term

n is number of terms

d is common difference between consecutive terms

We are told the 10th term is 45

Thus;

45 = a + (10 - 1)d

a + 9d = 45 - - - (1)

Formula for sum of n terms of an AP is;

S_n = (n/2)(2a + (n - 1)d)

Sum of first 10 terms is 270. Thus;

270 = (10/2)(2a + (10 - 1)d)

5(2a + 9d) = 270

2a + 9d = 270/5

2a + 9d = 54 - - - (2)

Solving both equations simultaneously gives;

a = 9 and d = 4

Thus;

First term = 9

Difference = 4

Sum of first 15 terms is;

S_15 = (15/2)(2(9) + (15 - 1)4)

S_15 = 7.5(18 + 56)

S_15 = 555

Read more on arithmetic progression at; https://brainly.com/question/7849474

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